040 - Greenjack

Some time ago, Farmer Joe made the mistake of gambling against one of his regular customers.

The game was Greenjack, a popular betting game in Serendipity. It is played with a deck of only 16 cards, divided into four suits: Red, Blue, Orange, and Green. There are four cards in each suit: Ace, King, Queen and Jack. Ace outranks King, which outranks Queen, which outranks Jack - except for the Green Jack, which outranks every other card.

If two cards have the same face value, then Red outranks Blue, which outranks Orange, which outranks Green, again except for the Green Jack, which outranks everything.

Farmer Joe, who is not the dealer, is dealt a card face up which both players can see. The dealer deals themselves a card, which they look at and then place face down. The dealer then makes three true statements which are capable of identifying which card is higher. If Farmer Joe correctly identifies which card is higher from the statements, he wins; otherwise he loses.

On this occasion, Farmer Joe was dealt the Blue King.

The dealer said:

1) My card would beat a Green King.
2) Knowing this, if my card is more likely to be a Jack than a Queen, then my card is a King. Otherwise, it isn't.
3) Given all of the information that you now know, if my card is more likely to beat yours than not, then my card is Red. Otherwise it isn't.

Farmer Joe got it wrong and lost the bet. Can you do better? Who holds the higher card?

037 - The Journey of Abernathy Gould

"Let me tell you a story," says Jacki Renquist as she leads Kent Dockland through the Logidyne Labs complex. "This happened during my grandfather's time."

"The great explorer, Abernathy Gould, came to western edge of a vast desert. She had with her her eight stalwart companions. Each of the nine travellers was driving an all-terrain car capable of travelling forty miles to the gallon - which was also the capacity of their cars' petrol tanks."

"When they reached the western edge of the desert, every car had a full tank of petrol, and each car carried nine extra gallon tins of petrol (that being the largest number of tins a single car was capable of carrying)."

"Under Gould's leadership, the nine travellers set out in a straight line east across the desert with the aim of Gould travelling the furthest distance east that she could manage, in the hope of finding.... something. All nine travellers returned safely, along with their cars, to the western edge of the desert at the conclusion of the journey. No additional petrol was acquired during the journey, no petrol was left unattended in the desert for any length of time (or, for that matter, with a car or driver to guard it), and none of the explorers travelled any distance on foot (as a journey on foot through the desert was said to spell certain death)."

"Gould later claimed that the distance she travelled into the desert was the greatest distance she could have achieved under the circumstances - which is lucky, as she only barely found what she was looking for."

Assuming Gould's claim is correct, how far east did she travel?

034 - Rational Pirates

Every morning the children of Serendipity thrill to the television adventures of Cap'n Redhook and his crew of perfectly rational sea-dogs as they sail the high seas in their clockwork ship The Razor of Occam.

Redhook's gang have an unusual way of dividing loot. The eldest pirate (in this case, Redhook) gets to propose a method of sharing the loot, and then all pirates (including the eldest) take a vote.  If a majority of pirates vote against the proposed split, the proposer gets thrown to the sharks, and the new eldest pirate proposes a new split, and so on until a split of loot is accepted.

In today's episode - Attack of the Cybersquid - Cap'n Redhook and his gang have looted 100 pieces o' eight from their nemesis, Admiral Goldbelly.  When it comes time to split the loot, what is the largest number of pieces o' eight Redhook can retain for himself?

Additional information:
* There are five pirates in Redhook's crew, including Redhook.
* All five pirates will vote so as to maximise their personal gain.  None are bothered by feeding their crewmembers to the sharks.
* Pieces o' eight can't be divided into fractions - the number of pieces o' eight each pirate gets must be an integer.
* Tied votes are resolved in favour of the proposer.

031 - Crackling

Farmer Joe keeps jars full of pre-prepared pork crackling to serve as entrees at Farmer Joe's BBQ Porkatorium.  One jar contains honey-marinated crackling, one jar contains peppered crackling, and one contains a mixture of both.

Unfortunately, Zephyr Cantrell, a regular customer with an odd sense of humour, has switched the labels on Farmer Joe's crackling jars.  According to Zephyr, each of the three jars now bears an incorrect label.  The three labels are "Honey-Marinated", "Peppered" and "Mixed".

Farmer Joe is keen not to waste any of his beloved pork crackling.  Unfortunately, the only way to tell honey-marinated crackling from peppered crackling is to taste it.

From the jar bearing which label should Farmer Joe taste a piece of crackling in order to correctly re-label all three jars?

029 - The Devices of Serendipity

Although there are, to date, 53 known Devices, only five are on display in the Serendipity Museum of Local History.

They are stored in a line of five display cases in a high security area of the museum, numbered 1 to 5 from left to right. Each of the five, as is the case with all known Devices, is marked with one of the runic characters of the local ancient language, and each possesses a single unique unexplained property.

1) There are two cases between a Device that emits random ultrasonic noises when exposed to sunlight, and the Device induced by Agnes Tutwillow on its right.

2) The Device that determines the number of iron molecules within 3.8 metres is in the case directly to the left of the Device induced by Yolanda Harkness.

3) There is one case between the Device that anaesthetises its holder, and the Device induced by Jonathan Horacek on its left.

4) The device induced by Brierly Smith is next to The Wheel.

5) The hole punch is not in the fifth case.

6) The Device that makes documents unintelligible is directly to the right of the protractor.

7) The Crossroads is not in the first case.

8) There are two cases between the audio cassette and the protractor.

9) The Crossroads is next to the hole punch.

10) The Knot is next to the pocket calculator.

11) There are two cases between the Device induced by Emilio Argento and The Bear.

12) There is one case between the device induced by Agnes Tutwillow and The Bear on the left.

13) The Wheel is not in the first case.

14) Although one of the Devices boils any liquid it is immersed in, it is not the flashlight.

15) The Thorn is not the pocket calculator.

What does The Knot look like, what does it do, which case is it in, and who induced it?

014 - Logidyne Hats

Logidyne Labs, a research and development company based in the city of Serendipity, is welcoming its newest round of recruits today. Before they can start work, Logidyne's head researcher Jacki Renquist subjects the three recruits to an unusual test.

Jacki instructs the three recruits to be seated, and then places a hat on the head of each recruit, such that each recruit can see all of the other hats, but none of them can see their own.

"Each hat is either white or blue," says Jacki. "There is at least one blue hat. You may not talk amongst yourselves, or communicate in any way. You may not remove your hat, or otherwise view its colour. None of you may start work until one of you correctly declares the colour of your own hat. If any of you incorrectly guess the colour of your hat, you will all three be fired. You have all been hired on the basis of your perfect command of rational thought, and therefore I am sure you will be able to start work today."

Jacki was correct and the recruits started work shortly thereafter.

How did they solve the test?

010 - Prisoners and Switches

Twenty-three prisoners are imprisoned in an unusual prison. They are to be imprisoned until the warden of the prison decides to set them free.

The warden meets the prisoners as they arrive and tells them about a special room in the prison. In the room are two switches, each of which can be set either an "up" position or a "down" position. The switches are not connected to anything, and the warden does not tell the prisoners whether either switch is currently "up" or "down".

"I am about to give you an hour to plan, talking amongst yourselves," says the warden to the prisoners. "After that, you will be incarcerated in separate cells with absolutely no means of communication."

"From time to time during your imprisonment, I will select one of you at random and escort that prisoner to the switch room. The prisoner I select must select one, and only one, of the two switches and reverse its position. Then he will be led back to his cell. This is the only way in which the switches will be flipped; they will always be in the position that the last prisoner to visit the room left them in."

"The method by which I select a prisoner will be totally random and it may result in the same prisoner being selected several times in a row."

"At any time that a prisoner is in the switch room, he or she may announce to me, 'We have all visited the switch room.' If that prisoner is correct, you will all be set free. If they are incorrect, you will all be executed in a particularly painful manner."

What is the fastest way for the prisoners to win their freedom, without the slightest risk of being executed?

009 - Proving The Rule

In front of you are four cards. Each card has a letter or number printed on the face-up side. The cards read, in order:

A
Z
4
9

In the deck that these cards have been dealt from, all of the cards have a number on one side and a letter on the other.

If I told you that there was a rule, that cards which have an "A" on one side always have a "4" on the other, which two cards would you turn over to attempt to disprove the rule?